Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D13×#64423 |
| Fitting, socle, derived, Hall | C72×C13 ⋊ C22×C3 |
| Hall | C7×D7×D13 ⋊ C3 |
| Hall | C13×#3861 ⋊ C22 |
| Hall | #3861 ⋊ C2×D13 |
| Sylow | C72 ⋊ C2×C3×D13 |
| Sylow | C13 ⋊ C2×#64423 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C13 | C22×C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
136 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#64418⋊C3, #37524901, #37524902, … |
| maximal normal subgroup of | #37524901, #37524902, ΓL(1,𝔽8)×D13×AGL(1,𝔽7), … |
| maximal quotient of | D13×#11725076, C3×D13×#64423, D13×C3⋊#64423, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 197);